Local field potentials (LFPs) are used to monitor the activity of large groups of neurons with macroelectrodes. Historically traditional linear statistical analysis techniques based on second order moments have been used to analyze these signals. We describe a new method based on power demodulation for estimating the instantaneous firing rate that is common to the neural activity of the most prominent neurons sensed by the electrodes. Correlated firing rates among neighboring neurons are common in many neurological structures and pathologies such as tremor. We validate our estimator with a Monte Carlo simulation based on a novel statistical model of LFPs. Our results show that the power demodulation approach can achieve a correlation of >0.80 with the common firing rate. This suggests that it may be possible to estimate the common intensity of a group neurons in recordings which are too noisy or contain too many neurons to apply spike detection or spike sorting algorithms.